code: def node_connectivity(G, s=None, t=None, flow_func=None):
      r"""Returns node connectivity for a graph or digraph G.
  
      Node connectivity is equal to the minimum number of nodes that
      must be removed to disconnect G or render it trivial. If source
      and target nodes are provided, this function returns the local node
      connectivity: the minimum number of nodes that must be removed to break
      all paths from source to target in G.
  
      Parameters
      ----------
      G : NetworkX graph
          Undirected graph
  
      s : node
          Source node. Optional. Default value: None.
  
      t : node
          Target node. Optional. Default value: None.
  
      flow_func : function
          A function for computing the maximum flow among a pair of nodes.
          The function has to accept at least three parameters: a Digraph,
          a source node, and a target node. And return a residual network
          that follows NetworkX conventions (see :meth:`maximum_flow` for
          details). If flow_func is None, the default maximum flow function
          (:meth:`edmonds_karp`) is used. See below for details. The
          choice of the default function may change from version
          to version and should not be relied on. Default value: None.
  
      Returns
      -------
      K : integer
          Node connectivity of G, or local node connectivity if source
          and target are provided.
  
      Examples
      --------
      >>> # Platonic icosahedral graph is 5-node-connected
      >>> G = nx.icosahedral_graph()
      >>> nx.node_connectivity(G)
      5
  
      You can use alternative flow algorithms for the underlying maximum
      flow computation. In dense networks the algorithm
      :meth:`shortest_augmenting_path` will usually perform better
      than the default :meth:`edmonds_karp`, which is faster for
      sparse networks with highly skewed degree distributions. Alternative
      flow functions have to be explicitly imported from the flow package.
  
      >>> from networkx.algorithms.flow import shortest_augmenting_path
      >>> nx.node_connectivity(G, flow_func=shortest_augmenting_path)
      5
  
      If you specify a pair of nodes (source and target) as parameters,
      this function returns the value of local node connectivity.
  
      >>> nx.node_connectivity(G, 3, 7)
      5
  
      If you need to perform several local computations among different
      pairs of nodes on the same graph, it is recommended that you reuse
      the data structures used in the maximum flow computations. See
      :meth:`local_node_connectivity` for details.
  
      Notes
      -----
      This is a flow based implementation of node connectivity. The
      algorithm works by solving $O((n-\delta-1+\delta(\delta-1)/2))$
      maximum flow problems on an auxiliary digraph. Where $\delta$
      is the minimum degree of G. For details about the auxiliary
      digraph and the computation of local node connectivity see
      :meth:`local_node_connectivity`. This implementation is based
      on algorithm 11 in [1]_.
  
      See also
      --------
      :meth:`local_node_connectivity`
      :meth:`edge_connectivity`
      :meth:`maximum_flow`
      :meth:`edmonds_karp`
      :meth:`preflow_push`
      :meth:`shortest_augmenting_path`
  
      References
      ----------
      .. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms.
          http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
  
      """
      if (s is not None and t is None) or (s is None and t is not None):
          raise nx.NetworkXError(
              "Both source and target must be specified."
          )
  
      # Local node connectivity
      if s is not None and t is not None:
          if s not in G:
              raise nx.NetworkXError(f"node {s} not in graph")
          if t not in G:
              raise nx.NetworkXError(f"node {t} not in graph")
          return local_node_connectivity(G, s, t, flow_func=flow_func)
  
      # Global node connectivity
      if G.is_directed():
          if not nx.is_weakly_connected(G):
              return 0
          iter_func = itertools.permutations
          # It is necessary to consider both predecessors
          # and successors for directed graphs
  
          def neighbors(v):
              return itertools.chain.from_iterable(
                  [G.predecessors(v), G.successors(v)]
              )
  
      else:
          if not nx.is_connected(G):
              return 0
          iter_func = itertools.combinations
          neighbors = G.neighbors
  
      # Reuse the auxiliary digraph and the residual network
      H = build_auxiliary_node_connectivity(G)
      R = build_residual_network(H, "capacity")
      kwargs = {"flow_func": flow_func, "auxiliary": H, "residual": R}
  
      # Pick a node with minimum degree
      # Node connectivity is bounded by degree.
      v, K = min(G.degree(), key=itemgetter(1))
      # compute local node connectivity with all its non-neighbors nodes
      for w in set(G) - set(neighbors(v)) - {v}:
          kwargs["cutoff"] = K
          K = min(K, local_node_connectivity(G, v, w, **kwargs))
      # Also for non adjacent pairs of neighbors of v
      for x, y in iter_func(neighbors(v), 2):
          if y in G[x]:
              continue
          kwargs["cutoff"] = K
          K = min(K, local_node_connectivity(G, x, y, **kwargs))
  
      return K
  
file_path: networkx/networkx/algorithms/connectivity/connectivity.py
imports: import itertools
  from operator import itemgetter
  import networkx
  from networkx.algorithms.flow import boykov_kolmogorov, build_residual_network, dinitz, edmonds_karp, shortest_augmenting_path
  from .utils import build_auxiliary_edge_connectivity, build_auxiliary_node_connectivity
label_desc: Use image node_id 2 for calling a global function with example usage: node_connectivity(G, s, t, flow_func) and returns: K, local_node_connectivity, int, itertools, int